Sure, let's start by calculating the area of the square that has each side of length 3 units.
The area of a square is given by the formula:
\[ \text{Area of Square} = (\text{side length})^2 \]
For our square with a side length of 3 units:
\[ \text{Area of Square} = 3^2 = 9 \text{ square units} \]
Next, we need to draw and label a rectangle that has a smaller area than 9 square units. To do this, we choose dimensions for the rectangle such that the product of its length and width is less than 9.
Let's consider a rectangle with the following dimensions:
- Length \(l\) = 2 units
- Width \(w\) = 1 unit
Now, we can calculate the area of this rectangle:
\[ \text{Area of Rectangle} = l \times w = 2 \times 1 = 2 \text{ square units} \]
Clearly, 2 square units is less than 9 square units, so our rectangle does indeed have a smaller area than the square.
To draw and label this rectangle, you would draw a figure with the following characteristics:
- The rectangle should be 2 units long on the horizontal side (length) and 1 unit wide on the vertical side (width).
- It is a good practice to include labels on the drawing that indicate the dimensions; write "Length: 2" along the horizontal side and "Width: 1" along the vertical side.
- Ensure that the rectangle is drawn to scale in relation to the square, which means the length of the rectangle should appear two-thirds the length of a side of the square if they were drawn next to each other.
In conclusion, the area of the rectangle that has a smaller area than the area of the square is 2 square units.